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Winkler and Pasternak foundations effect on the free vibration of an orthotropic oval cylindrical shell with variable thickness
Author(s) -
Khalifa Ahmed M.
Publication year - 2015
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201400097
Subject(s) - shell (structure) , vibration , orthotropic material , curvature , ovality , transfer matrix , normal mode , vibration of plates , bending , transfer matrix method (optics) , matrix (chemical analysis) , structural engineering , mathematics , mathematical analysis , materials science , geometry , physics , acoustics , composite material , engineering , finite element method , optoelectronics , computer science , computer vision
In this paper, based on the framework of the Flügge's shell theory, the transfer matrix approach and the Romberg integration method, the vibration behavior of an elastic oval cylindrical shell with parabolically varying thickness along of its circumference resting on the Winkler‐Pasternak foundations is investigated. The theoretical analysis of the governing equations of the shell is formulated to overcome the mathematical difficulties of mode coupling of variable curvature and thickness of shell. Using the transfer matrix of the shell, the vibration equations based on the Winkler‐Pasternak foundations are written in a matrix differential equation of first order in the circumferential coordinate and solved numerically. The proposed model is applied to get the vibration frequencies and the corresponding mode shapes of the symmetrical and antisymmetrical vibration modes. The sensitivity of the vibration characteristics and bending deformations to the Winkler‐Pasternak foundations moduli, thickness variation, ovality and orthotropy of the shell is studied for different type‐modes of vibration.